Dictatorship mechanism

Part of the Politics and Economics series
Electoral systems
Comparison of electoral systems Social choice theory Mechanism design List (By country)
Single-winner methods Single vote-runoff methods Plurality (FPP) Two-round (US: Jungle primary) Related: Partisan primary Instant runoff (IRV) / Alternative vote (US: Ranked-choice/RCV) Condorcet methods Condorcet-IRV Minimax Kemeny–Young Nanson Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting Quadratic voting
Proportional representation Party-list Nonpartisan proportional representation List type Closed list Open list Panachage Localized list Apportionment Highest averages Largest remainders National remnant Biproportional Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Cumulative Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel voting (superposition) Coexistence Conditional Majority bonus (fusion) Compensatory Additional member (seat linkage) system (MMP, AV+) Vote linkage system (Scorporo, MBTV) Dual-member proportional Rural–urban proportional Majority jackpot Supermixed systems By ballot type Single vote Two vote Mixed ballot
Voting system criteria Spoiler-resistance Condorcet criterion Smith independence Spoiler independence Clone independence Strategy-resistance Lesser evil voting Binary independence Maskin monotonicity Later-no-harm Later-no-help Rational response Participation criterion Positive response Reinforcement criterion Reversal symmetry
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Fishburn's example Positive results Median voter theorem Condorcet's jury theorem May's theorem Campbell-Kelly theorem Harsanyi's utilitarian theorem Tournament sets Smith set Landau set Copeland set Split-cycle set Bipartisan set
Politics portal Economics portal
v t e

In social choice theory, a dictatorship mechanism is a degenerate voting rule or mechanism where the result depends on only one person's preferences, without considering any other voters. A serial dictatorship is similar, but also designates a series of "backup dictators", who break ties in the original dictator's choices when the dictator is indifferent.

Non-dictatorship is one of the necessary conditions in Arrow's impossibility theorem.^[1] In Social Choice and Individual Values, Kenneth Arrow defines non-dictatorship as:

There is no voter ${\displaystyle i}$ in {1, ..., n} such that, for every set of orderings in the domain of the constitution, and every pair of social states x and y, ${\displaystyle x\succeq _{i}y}$ implies ${\displaystyle x\succeq y}$.

Unsurprisingly, a dictatorship is a rule that does not satisfy non-dictatorship. Anonymous voting rules automatically satisfy non-dictatorship (so long as there is more than one voter).

When the dictator is indifferent between two or more best-preferred options, it is possible to choose one of them arbitrarily or randomly, but this will not be strictly Pareto efficient. A more efficient solution is to appoint a secondary dictator, who has a right to choose, from among all the first dictator's best options, the one that they most prefer. If the second dictator is also indifferent between two or more options, then a third dictator chooses among them, and so on; in other words, ties are broken lexicographically. This rule is called serial dictatorship^[2]: 6 or the priority mechanism.

The priority mechanism is sometimes used in problems of house allocation. For example, when allocating dormitory rooms to students, it is common for academic administrators to care more about avoiding effort than about the students' well-being or fairness. Thus, students are often assigned a pre-specified priority order (e.g. by age, grades, distance, etc.) and is allowed to choose their most preferred room from the available ones.

Dictatorships often crop up as degenerate cases or exceptions to theorems, e.g. Arrow's theorem. If there are at least three alternatives, dictatorship is the only ranked voting rule that satisfies unrestricted domain, Pareto efficiency, and independence of irrelevant alternatives. Similarly, by Gibbard's theorem, when there are at least three candidates, dictatorship is the only strategyproof rule.

Satisfied criteria include:

• Perfect decisiveness: there is no possibility of a tied vote, assuming some selected voter has expressed a preference.
• Strategyproofness: there is never any advantage to tactical voting.

Failed criteria include:

• Determinism: the results depend on chance.
• Majority-rule: even if a single candidate has support from a majority in every subelection, that candidate may lose.